(x+1)(4x-56)=48

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Solution for (x+1)(4x-56)=48 equation: 


Simplifying
(x + 1)(4x + -56) = 48

Reorder the terms:
(1 + x)(4x + -56) = 48

Reorder the terms:
(1 + x)(-56 + 4x) = 48

Multiply (1 + x) * (-56 + 4x)
(1(-56 + 4x) + x(-56 + 4x)) = 48
((-56 * 1 + 4x * 1) + x(-56 + 4x)) = 48
((-56 + 4x) + x(-56 + 4x)) = 48
(-56 + 4x + (-56 * x + 4x * x)) = 48
(-56 + 4x + (-56x + 4x2)) = 48

Combine like terms: 4x + -56x = -52x
(-56 + -52x + 4x2) = 48

Solving
-56 + -52x + 4x2 = 48

Solving for variable 'x'.

Reorder the terms:
-56 + -48 + -52x + 4x2 = 48 + -48

Combine like terms: -56 + -48 = -104
-104 + -52x + 4x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-104 + -52x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-26 + -13x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-26 + -13x + x2)' equal to zero and attempt to solve:

Simplifying
-26 + -13x + x2 = 0

Solving
-26 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -13x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + -13x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -13x + x2 = 0 + 26
-13x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
-13x + x2 = 26

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 26 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 26 + 42.25

Combine like terms: 26 + 42.25 = 68.25
42.25 + -13x + x2 = 68.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(x + -6.5) equal to 8.261355821 and -8.261355821.


Subproblem 1
x + -6.5 = 8.261355821

Simplifying
x + -6.5 = 8.261355821

Reorder the terms:
-6.5 + x = 8.261355821

Solving
-6.5 + x = 8.261355821

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 8.261355821 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 8.261355821 + 6.5
x = 8.261355821 + 6.5

Combine like terms: 8.261355821 + 6.5 = 14.761355821
x = 14.761355821

Simplifying
x = 14.761355821


Subproblem 2
x + -6.5 = -8.261355821

Simplifying
x + -6.5 = -8.261355821

Reorder the terms:
-6.5 + x = -8.261355821

Solving
-6.5 + x = -8.261355821

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -8.261355821 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -8.261355821 + 6.5
x = -8.261355821 + 6.5

Combine like terms: -8.261355821 + 6.5 = -1.761355821
x = -1.761355821

Simplifying
x = -1.761355821


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.761355821, -1.761355821}
Solution
x = {14.761355821, -1.761355821}

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